I haven't been following the forepetessake saga, but if you care about DOF, then you should be comparing a m43 35-100/2.8 to a FF 70-200/5.6. Similar issues with noise.

There's no good reason to multiply the focal length by two, but leave the f-stop unchanged.

Very true. However the argument that if someone made an FF 70-200/5.6 it would be the same size and weight as the 35-100 is wrong. Such lenses were made (in the MF era) and they were larger and heavier. Going for a more extreme example, could anyone make a 200-600 lens, even a very slow one (e.g. wide open f11 at the 600 end) to the size of the Panasonic 100-300? Towards the longer zoom range, the mm count matters. There are a lot of compact superzoom cameras out there going to equivalent 600-800mm ranges with physically very short lenses because their real FL are in the 100+mm range so they can be built to not much more than 100mm long. To match the FoV in FF you will need to build a 600mm lens to 100mm long. You cannot do that no matter how slow you go.

So the sensor size does matter, in some cases at least, in lens size.

The Canon 70-200/2.8 is 1490g, while the f/4 is 760g. One stop halves the weight. An f/5.6 is likely to be substantially smaller.

The Panasonic 35-100/2.8 is 360g. A FF 70-200/5.6 might be heavier than that, but not by a whole lot. In any event, the original comparison, which suggested a FF lens would be about 4x the weight of an equivalent m43 lens, is highly misleading, at best.